Lectures on P-Adic L-Functions. (AM-74)
( Annals of Mathematics Studies )
Publication series ：Annals of Mathematics Studies
Author： Iwasawa Kinkichi
Publisher： Princeton University Press
Publication year： 2016
E-ISBN: 9781400881703
P-ISBN(Paperback): 9780691081120
Subject： O156.2 theory of algebraic numbers
Keyword： 数论,数学
Language： ENG
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Description
An especially timely work, the book is an introduction to the theory of p-adic L-functions originated by Kubota and Leopoldt in 1964 as p-adic analogues of the classical L-functions of Dirichlet.
Professor Iwasawa reviews the classical results on Dirichlet's L-functions and sketches a proof for some of them. Next he defines generalized Bernoulli numbers and discusses some of their fundamental properties. Continuing, he defines p-adic L-functions, proves their existence and uniqueness, and treats p-adic logarithms and p-adic regulators. He proves a formula of Leopoldt for the values of p-adic L-functions at s=1. The formula was announced in 1964, but a proof has never before been published. Finally, he discusses some applications, especially the strong relationship with cyclotomic fields.
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